Is home biasness common among modern investors? To which extent do Swedish investors diversify their investments on an international level? Does home biasness negatively affect the investors performance? To answer these questions, correlation tests of various international indices ranging over four different time periods are conducted, in order to see if correlation between markets are stronger today than before, as stronger correlation would render diversification less useful. To enhance the study, the holdings of the top ten Swedish funds, measured in fund capital according to Morningstar, is reviewed, based on data collected per 2014-12-31 from the Swedish Financial Supervisory Agency (FI). This gives an overview of how the funds diversify their investments internationally, these funds will in turn represent the average Swedish investor in the thesis. By constructing a bullet curve from a set of international indices, the author will analyse to which grade international diversification is useful. The results are that international diversification isn’t as beneficial as theory suggests it is. The reason for it may be due to stronger correlation between international markets in the past 15 years. Most of the Swedish funds tends to be rather home biased in their investments, as about a quarter of the holdings usually are placed in Swedish assets, and in accordance with the results of the indices development, the more home biased they are to Sweden, the better they tend to perform. / Hur vanligt är egentligen home biasness hos den moderna investeraren? Till vilken grad diversifierar egentligen den vanliga Svenska investeraren sina tillgångar internationellt? Påverkar en eventuellt inhemskt investeringsfilosofi investeraren negativt? Korrelationstester för olika världsindex kommer utföras, så att en överskådade blick kan fås över hur världsmarknader rör sig allt mer symmetriskt, då starkare symmetri mellan marknader minskar nyttan av internationell diversifiering. Data om innehav från Sveriges topp tio fonder, sett till fondförmögenhet utifrån Morningstar, har samlats från finansinspektionen per 2014-12-31. Dessa fonder ska representera den typiske Svenska investeraren och dess diversifieringsvanor. Genom att ha samlat data från ett flertal internationella index har effektiv front samt en fiktiv kombination av index skapats för att få fram huruvida avkastning i relation till risk ökar genom internationell diversifiering. Denna kombination av index jämförs sedan mot utveckling av en handfull internationellt samlade index för att se om diversifiering förbättrar avkastningen i relation till risk. Resultatet säger att det index som är mest diversifierade inte är så gynnsamt som teorin påstår. Anledningen till detta kan bero på den ökade korrelationen bland aktiemarknader idag jämfört med för 15 år sedan. De flesta Svenska fonderna har en större andel av sitt innehav i Svenska värdepapper och överlag, förutom diverse undantag, så har det gynnat dessa fonder i avkastning sett till risk.

The Dynamic Conditional Correlation (DCC) model proposed by Engle (2002) has become one of the most popular models for the analysis of multivariate financial time series. Yet, the impact of temporal aggregation on the DCC estimates has not yet been rigorously investigated. This thesis examines the changes of DCC estimates when the intraday returns are aggregated from 5-minutes to 270-minutes returns using Taiwanese eight industry index returns from Jan. 2, 2004 to Dec. 31, 2006. Our empirical analysis finds that dynamic correlation coefficients between the 8 industry index returns are all positive and time-varying. Further, Electronic and Building indices seem to have high correlation with other industry indices whereas plastics has a lower correlation with others. What is more important, all return series have higher conditional correlation for lower frequencies. In other words, temporary aggregation will increase the conditional correlation. This thesis also seeks to categorize the loan accounts of small- and medium-scale corporations according to their respective business sectors and calculate the monthly returns and standard deviation of the bank loans according to the groups of sample of credit records from each sector, with the purpose of establishing the efficient frontier of the loan combinations of the banks and estimation the dynamic conditional correlation to discover the optimal crediting policy. It is expected that the discussion using the model presented in the thesis may provide the basis for financial institutions as they establish their respective crediting policies.

Many complex systems involve simultaneous optimization of two or more criteria, with uncertainty of system parameters being a key driver in decision making. In this thesis, we consider probabilistic bicriteria models in which we seek to operate a system reliably, keeping operating costs low at the same time. High reliability translates into low risk of uncertain events that can adversely impact the system. In bicriteria decision making, a good solution must, at the very least, have the property that the criteria cannot both be improved relative to it. The problem of identifying a broad spectrum of such solutions can be highly involved with no analytical or robust numerical techniques readily available, particularly when the system involves nontrivial stochastics. This thesis serves as a step in the direction of addressing this issue. We show how to construct approximate solutions using Monte Carlo sampling, that are sufficiently close to optimal, easily calculable and subject to a low margin of error. Our approximations can be used in bicriteria decision making across several domains that involve significant risk such as finance, logistics and revenue management. As a first approach, we place a premium on a low risk threshold, and examine the effects of a sampling technique that guarantees a prespecified upper bound on risk. Our model incorporates a novel construct in the form of an uncertain disrupting event whose time and magnitude of occurrence are both random. We show that stratifying the sample observations in an optimal way can yield savings of a high order. We also demonstrate the existence of generalized stratification techniques which enjoy this property, and which can be used without full distributional knowledge of the parameters that govern the time of disruption. Our work thus provides a computationally tractable approach for solving a wide range of bicriteria models via sampling with a probabilistic guarantee on risk. Improved proximity to the efficient frontier is illustrated in the context of a perishable inventory problem. In contrast to this approach, we next aim to solve a bicriteria facility sizing model, in which risk is the probability the system fails to jointly satisfy a vector-valued random demand. Here, instead of seeking a probabilistic guarantee on risk, we instead seek to approximate well the efficient frontier for a range of risk levels of interest. Replacing the risk measure with an empirical measure induced by a random sample, we proceed to solve a family of parametric chance-constrained and cost-constrained models. These two sampling-based approximations differ substantially in terms of what is known regarding their asymptotic behavior, their computational tractability, and even their feasibility as compared to the underlying "true" family of models. We establish however, that in the bicriteria setting we have the freedom to employ either the chance-constrained or cost-constrained family of models, improving our ability to characterize the quality of the efficient frontiers arising from these sampling-based approximations, and improving our ability to solve the approximating model itself. Our computational results reinforce the need for such flexibility, and enable us to understand the behavior of confidence bounds for the efficient frontier. As a final step, we further study the efficient frontier in the cost versus risk tradeoff for the facility sizing model in the special case in which the (cumulative) distribution function of the underlying demand vector is concave in a region defined by a highly-reliable system. In this case, the "true" efficient frontier is convex. We show that the convex hull of the efficient frontier of a sampling-based approximation: (i) can be computed in strongly polynomial time by relying on a reformulation as a max-flow problem via the well-studied selection problem; and, (ii) converges uniformly to the true efficient frontier, when the latter is convex. We conclude with numerical studies that demonstrate the aforementioned properties. / text

The dissertation examined the effect of cryptocurrencies on the portfolio risk-adjusted returns of traditional and alternative investments using daily arithmetic returns from August 2015 to October 2018 of traditional assets (South African stocks, bonds, currencies), alternative assets (commodities, South African real estate) and cryptocurrencies (Cryptocurrency index (CRIX) and ten other individual cryptocurrencies). This is worth investigating as cryptocurrencies have been performing well while the listed equities in South Africa and most alternative investments have been underperforming (Srilakshmi & Karpagam, 2017). The mean-variance analysis, the Sharpe ratio, the conditional value-at-risk (CVaR) and the mean-variance spanning techniques were employed to analyse the data. The spanning test carried out was the multivariate ordinary least squares (OLS) regression Wald test. The research findings showed that the inclusion of cryptocurrencies in a portfolio of investments improves the efficient frontier of the portfolio of investments and the portfolio of investments risk-adjusted returns. Moreover, the findings suggested that cryptocurrencies are good portfolio diversification assets. However, investments in cryptocurrencies should be made with caution as the risks of investments are high in relation to traditional and alternative investments. The findings of this study advocate for individual and institutional investors to include cryptocurrencies within their South African portfolio of traditional and alternative investments.

<p>In this thesis, portfolio optimisation is used to evaluate if a specific sample of portfolios have</p><p>a higher risk level or lower expected return, compared to what may be obtained through</p><p>optimisation. It also compares the return of optimised portfolios with the return of the original</p><p>portfolios. The risk analysis software Aegis Portfolio Manager developed by Barra is used for</p><p>the optimisations. With the expected return and risk level used in this thesis, all portfolios can</p><p>obtain a higher expected return and a lower risk. Over a six-month period, the optimised</p><p>portfolios do not consistently outperform the original portfolios and therefore it seems as</p><p>though the optimisation do not improve the return of the portfolios. This might be due to the</p><p>uncertainty of the expected returns used in this thesis.</p>

There are several authors Markowitz (1991), Elton and Gruber (1997) that discuss the main issues that an investor faces when investing, for example how to allocate resources among the variety of different securities. These issues have led to the discussion of portfolio theories, especially the Modern Portfolio Theory (MPT), which is developed by Nobel Prize awarded economist Harry Markowitz. This theory is the philosophical opposite of tradi-tional asset picking. The purpose of this thesis is to investigate if an investor can apply MPT in order to achieve a higher return than investing in an index portfolio. Combining a strong portfolio that beats the market in the longrun would be the ultimate goal for most investors. The theories that are used to analyze the problem and the empirical findings provide the essential concepts such as standard deviation, risk and return of the portfolio. Further, diversification, correlation and covariance are used to achieve the optimal risky portfolio. There will be a walk-through of the MPT, with the efficient frontier as the graphical guide to express the optimal risky portfolio. The methodology constitutes as the frame for the thesis. The quantitative method is used since the data input is gathered from historical data. This thesis is based on existing theories, and the deductive approach aims to use these theories in order to accomplish a valid and accurate analysis. The benchmark that is used to compare the results from the portfolio is the Stockholm stock exchange OMX 30. This index mimics and reflects the market as a whole. The portfolio will be reweighed at a preplanned schedule, each quarter to constantly obtain an optimal risky portfolio. The finding from this study indicates that the actively managed portfolio outperforms the passive benchmark during the selected timeframe. The outcome someway differs when evaluating the risk adjusted result and becomes less significant. The risk adjusted result does not provide any strong evidence for a greater return than index. Finally, with this finding, the authors can conclude by stating that an actively managed optimal risky portfolio with guidance of the MPT can surpass the OMX 30 within the selected timeframe.

This thesis investigates robust techniques for mean-variance (MV) portfolio optimization problems under the estimation risk in mean return. We evaluate the performance of the optimal portfolios generated by the min-max robust MV portfolio optimization model. With an ellipsoidal uncertainty set based on the statistics of the sample mean estimates, minmax robust portfolios equal to the ones from the standard MV model based on the nominal mean estimates but with larger risk aversion parameters. With an interval uncertainty set for mean return, min-max robust portfolios can vary significantly with the initial data used to generate the uncertainty set. In addition, by focusing on the worst-case scenario in the mean return uncertainty set, min-max robust portfolios can be too conservative and unable to achieve a high return. Adjusting the conservatism level of min-max robust portfolios can only be achieved by excluding poor mean return scenarios from the uncertainty set, which runs counter to the principle of min-max robustness. We propose a CVaR robust MV portfolio optimization model in which the estimation risk is measured by the Conditional Value-at-Risk (CVaR). We show that, using CVaR to quantify the estimation risk in mean return, the conservatism level of CVaR robust portfolios can be more naturally adjusted by gradually including better mean return scenarios. Moreover, we compare min-max robust portfolios (with an interval uncertainty set for mean return) and CVaR robust portfolios in terms of actual frontier variation, portfolio efficiency, and portfolio diversification. Finally, a computational method based on a smoothing technique is implemented to solve the optimization problem in the CVaR robust model. We numerically show that, compared with the quadratic programming (QP) approach, the smoothing approach is more computationally efficient for computing CVaR robust portfolios.

This thesis investigates robust techniques for mean-variance (MV) portfolio optimization problems under the estimation risk in mean return. We evaluate the performance of the optimal portfolios generated by the min-max robust MV portfolio optimization model. With an ellipsoidal uncertainty set based on the statistics of the sample mean estimates, minmax robust portfolios equal to the ones from the standard MV model based on the nominal mean estimates but with larger risk aversion parameters. With an interval uncertainty set for mean return, min-max robust portfolios can vary significantly with the initial data used to generate the uncertainty set. In addition, by focusing on the worst-case scenario in the mean return uncertainty set, min-max robust portfolios can be too conservative and unable to achieve a high return. Adjusting the conservatism level of min-max robust portfolios can only be achieved by excluding poor mean return scenarios from the uncertainty set, which runs counter to the principle of min-max robustness. We propose a CVaR robust MV portfolio optimization model in which the estimation risk is measured by the Conditional Value-at-Risk (CVaR). We show that, using CVaR to quantify the estimation risk in mean return, the conservatism level of CVaR robust portfolios can be more naturally adjusted by gradually including better mean return scenarios. Moreover, we compare min-max robust portfolios (with an interval uncertainty set for mean return) and CVaR robust portfolios in terms of actual frontier variation, portfolio efficiency, and portfolio diversification. Finally, a computational method based on a smoothing technique is implemented to solve the optimization problem in the CVaR robust model. We numerically show that, compared with the quadratic programming (QP) approach, the smoothing approach is more computationally efficient for computing CVaR robust portfolios.

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<p>There are several authors Markowitz (1991), Elton and Gruber (1997) that discuss the main issues that an investor faces when investing, for example how to allocate resources among the variety of different securities. These issues have led to the discussion of portfolio theories, especially the Modern Portfolio Theory (MPT), which is developed by Nobel Prize awarded economist Harry Markowitz. This theory is the philosophical opposite of tradi-tional asset picking.</p><p>The purpose of this thesis is to investigate if an investor can apply MPT in order to achieve a higher return than investing in an index portfolio. Combining a strong portfolio that beats the market in the longrun would be the ultimate goal for most investors.</p><p>The theories that are used to analyze the problem and the empirical findings provide the essential concepts such as standard deviation, risk and return of the portfolio. Further, diversification, correlation and covariance are used to achieve the optimal risky portfolio. There will be a walk-through of the MPT, with the efficient frontier as the graphical guide to express the optimal risky portfolio.</p><p>The methodology constitutes as the frame for the thesis. The quantitative method is used since the data input is gathered from historical data. This thesis is based on existing theories, and the deductive approach aims to use these theories in order to accomplish a valid and accurate analysis. The benchmark that is used to compare the results from the portfolio is the Stockholm stock exchange OMX 30. This index mimics and reflects the market as a whole. The portfolio will be reweighed at a preplanned schedule, each quarter to constantly obtain an optimal risky portfolio.</p><p>The finding from this study indicates that the actively managed portfolio outperforms the passive benchmark during the selected timeframe. The outcome someway differs when evaluating the risk adjusted result and becomes less significant. The risk adjusted result does not provide any strong evidence for a greater return than index. Finally, with this finding, the authors can conclude by stating that an actively managed optimal risky portfolio with guidance of the MPT can surpass the OMX 30 within the selected timeframe.</p>